Inside a new directory, create a data directory and docker-compose.yml with these rows:

version: '3'

services: 
  db:
    container_name: docker-local-mysql
    image: mysql:5.7.21
    volumes:
      - "./data:/var/lib/mysql"
    restart: always
    ports:
      - 3306:3306
    environment:
      MYSQL_ROOT_PASSWORD: password

To start the container, run docker-compose up -d. To stop & remove the container, run docker-compose down.

To connect from a MySql client use this:

Host: 127.0.0.1
Username: root
Password: password
Port: 3306

Docker-Compose mySql